American employers have a variety of job vacancies, piles of cash and countless well-qualified candidates. But despite a slowly improving economy, many companies remain reluctant to actually hire, stringing job applicants along for weeks or months before they make a decision.

If they ever do.

The number of job openings has increased to levels not seen since the height of the financial crisis, but vacancies are staying unfilled much longer than they used to — an average of 23 business days today compared to a low of 15 in mid-2009, according to a new measure of Labor Department data by the economists Steven J. Davis, Jason Faberman and John Haltiwanger.